Analytic Cross Sections for Substructure Lensing

The magnifications of the images in a strong gravitational lens system are sensitive to small mass clumps in the lens potential; this effect has been used to infer the amount of substructure in galaxy dark matter halos. I study the theory of substructure lensing to identify important general features, and to compute analytic cross sections that will facilitate further theoretical studies. I show that the problem of a clump anywhere along the line of sight to a lens can be mapped onto an equivalent problem of a clump in a simple convergence and shear field; clumps at arbitrary redshifts are therefore not hard to handle in calculations. For clumps modeled as singular isothermal spheres (SIS), I derive simple analytic estimates of the cross section for magnification perturbations of a given strength. The results yield two interesting conceptual points. First, lensed images with positive parity are always made brighter by SIS clumps; images with negative parity can be brightened but are much more likely to be dimmed. Second, the clumps need not lie within the lens galaxy; they can be moved in redshift by several tenths and still have a significant lensing effect. Isolated small halos are expected to be common in hierarchical structure formation models, but it is not yet known whether they are abundant enough compared with clumps inside lens galaxies to affect the interpretation of substructure lensing.Comment: accepted in ApJ; minor text changes from original versio

Gravitational Lenses With More Than Four Images: I. Classification of Caustics

We study the problem of gravitational lensing by an isothermal elliptical density galaxy in the presence of a tidal perturbation. When the perturbation is fairly strong and oriented near the galaxy's minor axis, the lens can produce image configurations with six or even eight highly magnified images lying approximately on a circle. We classify the caustic structures in the model and identify the range of models that can produce such lenses. Sextuple and octuple lenses are likely to be rare because they require special lens configurations, but a full calculation of the likelihood will have to include both the existence of lenses with multiple lens galaxies and the strong magnification bias that affects sextuple and octuple lenses. At optical wavelengths these lenses would probably appear as partial or complete Einstein rings, but at radio wavelengths the individual images could probably be resolved.Comment: 30 pages, including 12 postscript figures; accepted for publication in Ap

Review of computational thermal-hydraulic modeling

Corrosion of heat transfer tubing in nuclear steam generators has been a persistent problem in the power generation industry, assuming many different forms over the years depending on chemistry and operating conditions. Whatever the corrosion mechanism, a fundamental understanding of the process is essential to establish effective management strategies. To gain this fundamental understanding requires an integrated investigative approach that merges technology from many diverse scientific disciplines. An important aspect of an integrated approach is characterization of the corrosive environment at high temperature. This begins with a thorough understanding of local thermal-hydraulic conditions, since they affect deposit formation, chemical concentration, and ultimately corrosion. Computational Fluid Dynamics (CFD) can and should play an important role in characterizing the thermal-hydraulic environment and in predicting the consequences of that environment,. The evolution of CFD technology now allows accurate calculation of steam generator thermal-hydraulic conditions and the resulting sludge deposit profiles. Similar calculations are also possible for model boilers, so that tests can be designed to be prototypic of the heat exchanger environment they are supposed to simulate. This paper illustrates the utility of CFD technology by way of examples in each of these two areas. This technology can be further extended to produce more detailed local calculations of the chemical environment in support plate crevices, beneath thick deposits on tubes, and deep in tubesheet sludge piles. Knowledge of this local chemical environment will provide the foundation for development of mechanistic corrosion models, which can be used to optimize inspection and cleaning schedules and focus the search for a viable fix

Formalism for testing theories of gravity using lensing by compact objects. III: Braneworld gravity

Braneworld gravity is a model that endows physical space with an extra dimension. In the type II Randall-Sundrum braneworld gravity model, the extra dimension modifies the spacetime geometry around black holes, and changes predictions for the formation and survival of primordial black holes. We develop a comprehensive analytical formalism for far-field black hole lensing in this model, using invariant quantities to compute all geometric optics lensing observables. We then make the first analysis of wave optics in braneworld lensing, working in the semi-classical limit. We show that wave optics offers the only realistic way to observe braneworld effects in black hole lensing. We point out that if primordial braneworld black holes exist, have mass M, and contribute a fraction f of the dark matter, then roughly 3e5 x f (M/1e-18 Msun)^(-1) of them lie within our Solar System. These objects, which we call "attolenses," would produce interference fringes in the energy spectra of gamma-ray bursts at energies ~100 (M/1e-18 Msun)^(-1) MeV (which will soon be accessible with the GLAST satellite). Primordial braneworld black holes spread throughout the universe could produce similar interference effects; the probability for "attolensing" may be non-negligible. If interference fringes were observed, the fringe spacing would yield a simple upper limit on M. Detection of a primordial black hole with M <~ 1e-19 Msun would challenge general relativity and favor the braneworld model. Further work on lensing tests of braneworld gravity must proceed into the physical optics regime, which awaits a description of the full spacetime geometry around braneworld black holes.Comment: 13 pages, 3 figures; accepted in PRD; expanded discussion of prospects for observing attolensing with GLAS

What Fraction of Gravitational Lens Galaxies Lie in Groups?

We predict how the observed variations in galaxy populations with environment affect the number and properties of gravitational lenses in different environments. Two trends dominate: lensing strongly favors early-type galaxies, which tend to lie in dense environments, but dense environments tend to have a larger ratio of dwarf to giant galaxies than the field. The two effects nearly cancel, and the distribution of environments for lens and non-lens galaxies are not substantially different (lens galaxies are slightly less likely than non-lens galaxies to lie in groups and clusters). We predict that about 20% of lens galaxies are in bound groups (defined as systems with a line-of-sight velocity dispersion sigma in the range 200 < sigma < 500 km/s), and another roughly 3% are in rich clusters (sigma > 500 km/s). Therefore at least roughly 25% of lenses are likely to have environments that significantly perturb the lensing potential. If such perturbations do not significantly increase the image separation, we predict that lenses in groups have a mean image separation that is about 0.2'' smaller than that for lenses in the field and estimate that 20-40 lenses in groups are required to test this prediction with significance. The tail of the distribution of image separations is already illuminating. Although lensing by galactic potential wells should rarely produce lenses with image separations theta >~ 6'', two such lenses are seen among 49 known lenses, suggesting that environmental perturbations of the lensing potential can be significant. Further comparison of theory and data will offer a direct probe of the dark halos of galaxies and groups and reveal the extent to which they affect lensing estimates of cosmological parameters.Comment: 32 pages, 6 embedded figures; accepted for publication in Ap

The Infrared Einstein Ring in the Gravitational Lens MG1131+0456 and the Death of the Dusty Lens Hypothesis

We have obtained and modeled new NICMOS images of the lens system MG1131+0456, which show that its lens galaxy is an H=18.6 mag, transparent, early-type galaxy at a redshift of about z_l = 0.85; it has a major axis effective radius R_e=0.68+/-0.05 arcsec, projected axis ratio b/a=0.77+/-0.02, and major axis PA=60+/-2 degrees. The lens is the brightest member of a group of seven galaxies with similar R-I and I-H colors, and the two closest group members produce sufficient tidal perturbations to explain the ring morphology. The host galaxy of the MG1131+0456 source is a z_s > 2 ERO (``extremely red object'') which is lensed into optical and infrared rings of dramatically different morphologies. These differences imply a strongly wavelength-dependent source morphology that could be explained by embedding the host in a larger, dusty disk. At 1.6 micron (H), the ring is spectacularly luminous, with a total observed flux of H=17.4 mag and a de-magnified flux of 19.3 mag, corresponding to a 1-2L_* galaxy at the probable source redshift of z_s > 2. Thus, it is primarily the stellar emission of the radio source host galaxy that produces the overall colors of two of the reddest radio lenses, MG1131+0456 and B~1938+666, aided by the suppression of optical AGN emission by dust in the source galaxy. The dusty lens hypothesis -- that many massive early-type galaxies with 0.2 < z_l < 1.0 have large, uniform dust opacities -- is ruled out.Comment: 27 pages, 8 COLOR figures, submitted to ApJ. Black and white version available at http://cfa-www.harvard.edu/castle

Observations of Lensed Relativistic Jets as a Tool of Constraining Lens Galaxy Parameters

The possibility of using lensed relativistic jets on very small angular scales to construct proper models of spiral lens galaxies and to independently determine the Hubble constant is considered. The system B0218+357 is used as an example to illustrate that there exists a great choice of model parameters adequately reproducing its observed large-scale properties but leading to a significant spread in the Hubble constant. The jet image position angle is suggested as an additional parameter that allows the range of models under consideration to be limited. It is shown that the models for which the jet image position angles differ by at least $40^o$ can be distinguished between themselves during observations on very small angular scales. The possibility of observing the geometric properties of lensed relativistic jets and measuring the superluminal velocities of knot images on time scales of several months with very long baseline space interferometers is discussed.Comment: 11 pages, 3 figures, Will be published in the Astronomy Letters, V.37, PP.483-490, 201

A Spectroscopic Study of the Environments of Gravitational Lens Galaxies

(Abridged) We present the first results from our spectroscopic survey of the environments of strong gravitational lenses. The lens galaxy belongs to a poor group of galaxies in six of the eight systems in our sample. We discover three new groups associated with the lens galaxies of BRI 0952-0115 (five members), MG 1654+1346 (seven members), and B2114+022 (five members). We more than double the number of members for another three previously known groups around the lenses MG 0751+2716 (13 total members), PG 1115+080 (13 total members), and B1422+231 (16 total members). We determine the kinematics of the six groups, including their mean velocities, velocity dispersions, and projected spatial centroids. The velocity dispersions of the groups range from 110 +170, -80 to 470 +100, -90 km/s. In at least three of the lenses -- MG0751, PG1115, and B1422 -- the group environment significantly affects the lens potential. These lenses happen to be the quadruply-imaged ones in our sample, which suggests a connection between image configuration and environment. The lens galaxy is the brightest member in fewer than half of the groups. Our survey also allows us to assess for the first time whether mass structures along the line of sight are important for lensing. We first show that, in principle, the lens potential may be affected by line-of-sight structures over a wide range of spatial and redshift offsets from the lens. We then quantify real line-of-sight effects using our survey and find that at least four of the eight lens fields have substantial interloping structures close in projection to the lens, and at least one of those structures (in the field of MG0751) significantly affects the lens potential.Comment: Accepted for publication in the Astrophysical Journal. Figure 6 posted as a JPEG image. Requires emulateapj.st